Volume Changes

Physics 313Professor Lee

CarknerLecture 19

Exercise #18 Steam Tables

Boiling water at low pressure From chart P = 75 kPa, T = 91.78 C and T = 100 kPa,

T = 99.63 C

Cover with heavy lid Plid = F/A = mg/r2 = [(4)(9.8)/()(0.1)2] = 1.25 kPa Now have a factor of 0.384 between table values

http://www.chempute.com/waspwin.htm

Solids

Solids will hold a volume even in conditions of low external pressure

Need to be able to accurately measure small changes to find expansivity and compressibility

Volume Expansivity How does the size of a a solid object change

with temperature? Need to find volume expansivity

For isotropic materials:

where is the linear expansivity:

= (1/L)(dL/dT) Note that some materials are non-isotropic

Optical Interferometer To find and thus need to measure

small change in linear dimension

Separate two semi-transparent plates with a ring of the material in question

Each interference fringe that moves past a reference point indicates ½ wavelength of changed size

Determining

If N fringes pass the field of view, than the change in size (from L0 to L) is:

The relative change is:

(L - L0)/L0 = ½N / L0

Or: = d/dT (½N / L0)

Variation of with T

Rises sharply with T and then

flattens out

Variations are only weakly

dependant on pressure (for solids)

Compressibility

How does volume change with pressure?

= -(1/V)(dV/dP)

Adiabatic compressibility is also isentropic

Determining s

The adiabatic compressibility can be found for a fluid by measuring the speed of sound (pressure) waves

For a crystal solid have to measure both shear and pressure waves

and S

How are and s related? by the heat capacities:

cP –cV = Tv2/

We can combine equations to get:

-S = Tv2/cP

Variations of with T

Unlike approaches a constant at 0 K

Values tend to rise linearly at higher T for solids

Liquids generally have an exponential rise of with T:

Liquids also have a linear increase of

with P

Heat Capacity at Constant Volume

Can find cV with Mayer relation How does cV (molar heat capacity) vary with

temperature?

At the Debye temperature, cV approaches 3R

For all substances, cV versus T curves have a similar shape, but each substance may have different Debye temperatures

Entropy and Heat Capacities

How are the entropy and heat capacities related?

dS = dQ/T

(dQ/dT) = T (dS/dT)

Can calculate entropy change from C:

Where C is CP or CV depending on if the process is isobaric or isochoric

The TS Diagram

Generally have solid at low T and low S and gas at high T and high S